Some classic examples are petty thefts where the victim has a heart attack, or a medical practitioner acts outside their legal authority (e.g., while unlicensed) or egregiously failing to act despite having a duty of care.
You have act with recklessness or criminal negligence (or, where a misdemeanor manslaughter rule exists, commit a misdemameanor that resulted in the death.) None of these, except some misdemeanors, require intentional wrongdoing.
In the trolley problem, you certainly can't be negligent (unless you own the trolley line or something). I'm not sure you could be called reckless either if your decision was meant to do the most good.
I think the minimal pair is something like losing control of a car and fatally swerving into another car because:
- you were driving like a maniac and hit ice==> culpable
- you were driving prudently for the overall conditions, but hit oil spilled on a dark road (or something else unforseeable) ==> not.